Information-Theoretic Error Bounds for Source Localization in Neural Sensing

Leighton Pate Barnes, Yuxin Guo, Alex Dytso, Pulkit Grover
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:2125-2133, 2026.

Abstract

We formulate a point-source localization problem in $d$ dimensions, where a source inside the ball of radius $R$ emits a signal that is picked up by various sensors located at the surface of the ball. For $d=3$, this can model problems in neural sensing, where a net of electroencephalography (EEG) or magnetoencephalography (MEG) sensors try to locate the source of a distinct neural event such as a seizure. For a power law decay model with exponent $\alpha>0$ for the sensors, we obtain a lower bound on the minimax risk for localizing the source that is asymptotically $\frac{d^2\sigma^2R^{2\alpha+2}}{n\alpha^2PK}$ under mean-squared error loss, where $\sigma^2$ is the noise variance, $P$ is the signal power, $K$ is the number of sensors, and $n$ is the number of independent measurements. In the case $d\leq 2(\alpha+1)$ with uniformly distributed sensor locations, we then give a matching upper bound, including getting the exact constant correct, for the asymptotic minimax rate in a neighborhood of the origin. We show that there is a phase transition at $d=2(\alpha+2)$, above which a certain Fisher information quantity is minimized at the boundary of the ball, and below which it is minimized at the origin. At the critical dimension $d=2(\alpha+2)$, the Fisher information is constant throughout the entire parameter space. For the special case $d=3$, we supplement and compare this information-theoretic analysis with a simulated forward EEG model that uses a realistic head model derived from population-averaged magnetic resonance imaging data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-barnes26a, title = { Information-Theoretic Error Bounds for Source Localization in Neural Sensing }, author = {Barnes, Leighton Pate and Guo, Yuxin and Dytso, Alex and Grover, Pulkit}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {2125--2133}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/barnes26a/barnes26a.pdf}, url = {https://proceedings.mlr.press/v300/barnes26a.html}, abstract = { We formulate a point-source localization problem in $d$ dimensions, where a source inside the ball of radius $R$ emits a signal that is picked up by various sensors located at the surface of the ball. For $d=3$, this can model problems in neural sensing, where a net of electroencephalography (EEG) or magnetoencephalography (MEG) sensors try to locate the source of a distinct neural event such as a seizure. For a power law decay model with exponent $\alpha>0$ for the sensors, we obtain a lower bound on the minimax risk for localizing the source that is asymptotically $\frac{d^2\sigma^2R^{2\alpha+2}}{n\alpha^2PK}$ under mean-squared error loss, where $\sigma^2$ is the noise variance, $P$ is the signal power, $K$ is the number of sensors, and $n$ is the number of independent measurements. In the case $d\leq 2(\alpha+1)$ with uniformly distributed sensor locations, we then give a matching upper bound, including getting the exact constant correct, for the asymptotic minimax rate in a neighborhood of the origin. We show that there is a phase transition at $d=2(\alpha+2)$, above which a certain Fisher information quantity is minimized at the boundary of the ball, and below which it is minimized at the origin. At the critical dimension $d=2(\alpha+2)$, the Fisher information is constant throughout the entire parameter space. For the special case $d=3$, we supplement and compare this information-theoretic analysis with a simulated forward EEG model that uses a realistic head model derived from population-averaged magnetic resonance imaging data. } }
Endnote
%0 Conference Paper %T Information-Theoretic Error Bounds for Source Localization in Neural Sensing %A Leighton Pate Barnes %A Yuxin Guo %A Alex Dytso %A Pulkit Grover %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-barnes26a %I PMLR %P 2125--2133 %U https://proceedings.mlr.press/v300/barnes26a.html %V 300 %X We formulate a point-source localization problem in $d$ dimensions, where a source inside the ball of radius $R$ emits a signal that is picked up by various sensors located at the surface of the ball. For $d=3$, this can model problems in neural sensing, where a net of electroencephalography (EEG) or magnetoencephalography (MEG) sensors try to locate the source of a distinct neural event such as a seizure. For a power law decay model with exponent $\alpha>0$ for the sensors, we obtain a lower bound on the minimax risk for localizing the source that is asymptotically $\frac{d^2\sigma^2R^{2\alpha+2}}{n\alpha^2PK}$ under mean-squared error loss, where $\sigma^2$ is the noise variance, $P$ is the signal power, $K$ is the number of sensors, and $n$ is the number of independent measurements. In the case $d\leq 2(\alpha+1)$ with uniformly distributed sensor locations, we then give a matching upper bound, including getting the exact constant correct, for the asymptotic minimax rate in a neighborhood of the origin. We show that there is a phase transition at $d=2(\alpha+2)$, above which a certain Fisher information quantity is minimized at the boundary of the ball, and below which it is minimized at the origin. At the critical dimension $d=2(\alpha+2)$, the Fisher information is constant throughout the entire parameter space. For the special case $d=3$, we supplement and compare this information-theoretic analysis with a simulated forward EEG model that uses a realistic head model derived from population-averaged magnetic resonance imaging data.
APA
Barnes, L.P., Guo, Y., Dytso, A. & Grover, P.. (2026). Information-Theoretic Error Bounds for Source Localization in Neural Sensing . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:2125-2133 Available from https://proceedings.mlr.press/v300/barnes26a.html.

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